Michele Bachmann signs a copy of her book, "Core of Conviction," at Barnes & Noble in Sioux City, Iowa.

By Jamie Novogrod, NBC News

COUNCIL BLUFFS, Iowa – Michele Bachmann’s campaign kept up its criticisms of Newt Gingrich Sunday, hours after the former Speaker of the House won the support of the New Hampshire Union Leader newspaper, a key endorsement in the country’s first in the nation primary state.

“There’s a lot of different endorsements that come from a lot of papers, and the main endorsement that I’m looking forward to is the one here in Iowa on January 3rd in the caucuses,” Bachmann said.

The remarks came during a visit to a Barnes & Noble store in Sioux City, where Bachmann signed copies of her new book, “Core of Conviction,” for about 75 supporters.

But Bachmann’s campaign staff took a harder line, telling NBC News that a sentence in the newspaper’s endorsement – “Newt Gingrich is by no means the perfect candidate” – points to both a problem with Gingrich, and the logic for supporting him.

"We shouldn’t settle. More than any time, this is an election that we need to hold out for the ideal, like Michele,” campaign spokeswoman Alice Stewart said.

A back and forth between the Bachmann and Gingrich teams has been going on since Tuesday’s CNN debate in Washington, where Gingrich seemed to call for a path to citizenship for longtime illegal residents of the United States.

“Here he is outlining an amnesty plan,” Stewart said Sunday of Gingrich.